The Karve brass with 2 plates would keep you close to your $100 limit. It is the second razor I bought (B & C plates SB). As I have progressed I now only use the "G" SB & "F" OC plates. It is a fine razor that will allow you to progress just about as far as you want to in efficiency.
I'll through out one other idea. You can buy the Muhle R41 cap and plate (no handle) for $25 at Maggard. Some would have you believe this is a meat clever, but it is far from that. I can't think of a razor I have had more fun using. It is very efficient, but also very smooth as well. For a very small investment it will help you gauge your technique as you continue to progress. The head is made of zamak but the cap post is brass on the newer models. Most failures with zamak razors happen to the cap posts.
I'll through out one other idea. You can buy the Muhle R41 cap and plate (no handle) for $25 at Maggard. Some would have you believe this is a meat clever, but it is far from that. I can't think of a razor I have had more fun using. It is very efficient, but also very smooth as well. For a very small investment it will help you gauge your technique as you continue to progress. The head is made of zamak but the cap post is brass on the newer models. Most failures with zamak razors happen to the cap posts.